Unlike conventional deep neural network (DNN) based activity detection [1]}, where the adopted activation function is a black box that has no explicit physical meaning, the designed denoiser in (REF ) of the proposed FAT-DL network is equivalent to the activation function. The designed denoiser has an explicit physical meaning, this is because the denoiser can promote \(\hat{\mathbf {S}}\)  sparser by minimizing the mean-squared-error (MSE) in each iteration. In this context, the proposed FAT-DL network requires less low-dimensional training data and shorter training time. However, in [1]}, to train the black box, it requires large training data and training time, which are often scarce in 6G wireless networks due to the fact that the fading channel is time-varying and the activity status of the devices changes over the time slots. In addition, the proposed FAT-DL network is obtained by unfolding an
iterative algorithm, thus its performance can be rigorously analyzed through combing the specific denoiser in (REF ) with the state evolution [3]}, which will be discussed in the future work.
